Air is heated as it is flowing through a duct of 15 m in length and 0.1 m in diameter. The coefficient of friction in the duct is 0.01. The stagnation temperature and the stagnation pressure at the inlet of the duct are 500 K and 200 kPa, respectively. The total force acting on the duct is 50 N. It is found that a normal shock wave stands at a location 5 m from the entrance of the duct. The mass flow rate through the duct is 2 kg/s. If the exit pressure is 100 kPa, find the exit Mach number and rate of heat transfer. (METU 1985)